Means for determining aerodynamic states of aircraft



Jan., 16, wm w. N. FINDLEY 39539303 MEANS FOR DETERMINING AERODYNAMIC STATES OF' AIRCRAFT Filed March 22, 1944 2 Sheets-Sheet 2 TTORNEYS Patented Jan. 16, 1951 MEANS FOR DETERMINNG AERODYNAWC STATES 0F AIRCRAFT William Nichols Findley, Urbana, 11i., assignor to Robert C. Brown, Jr., Highland Park, lll., as

trustee Application March 22, 1944, Serial No. 527,660

4 Claims. (Cl. i3-178) My invention relates to instrumentalities for revealing aerodynamic factors in the course of aircraft ight and is particularly directed to the problem of ascertaining the instant effect of all the forces acting on the aircraft.

The large amount of Work that has been done in the field of aerodynamics reveals that a number of factors, forces, eects, and various values and derivatives employed by aeronautical engineers vary concurrently `with the flight behavior or what may be termed the aerodynamic state of an aircraft. Among these the following may be listed: the Weight of the aircraft, fuel load, pay load, thrust, Wing loading, accelerations, structural strain, internal stresses, attitude, dimensions of the aircraft, mass density of the air, true air speed, pressures renecting air speed, dynamic pressure, angle of attack, lift coefficient, drag coefficient, moment coeiiicient, and position of centerY pressure. Values representing selective items from the above list are commonly combined mathematically to express relationships involved in aircraft design and flight. Such a grouping of values may, if desired, be so compiete as to express or reflect the net effect of all the forces that determine the .behavior of the aircraft. Since all of the items are involved in the night behavior or aerodynamic state of the aircraft, an expression comprising a few terms selected from the list may reflect other of the listed values and such an expression may in some instances be employed primarily to determine some quantity apart from the constituent terms.

The general object of my invention is to arrive at such an expression made up of selected terms which may be employed to ascertain, indicate or reflect the aerodynamic state of the aircraft and which may, in effect, be embodied in some suitable responsive means for determining instant changes in the Value of the expression in the course of aircraft flight either for following the instantvariations in the aerodynamic state of the aircraft or for indicating the instant value cf concurrent quantities not represented specifically by the terms of the expression.

For the purpose of the present disclosure I shall describe the invention as embodied in an aircraft instrument for continuously indicating the instant values of a function representing or related to the aerodynamic state of the aircraft. Since the invention has special utility for indieating the proximity to stall conditions, I elect to describe an instrument designed specifically to serve as a stall-Warning device.

Such a Warning device may serve to reduce accidents befalling fliers of limited experience, such as students in training and private fliers Who taire to the air only occasionally. Records of the Civil Aeronautics Administration show that the largest percentage of accidents occurring with this class of fliers are accidents resulting from stalling of aircraft under conditions precluding recovery.

A stali-warning instrument is also of service to experienced pilots especially since military and transport planes often must be flown with low margins of safety necessitating taire-off and landing under conditions of high lift coefficient, the coefficient being near the stall point. A reliable instrument for indicating the proximity of the aerodynamic state of the aircrait'to a stall condition will apprise the pilot of the instant avail#- ability margin of safety. Knowledge of the margin of safety is especially important in flying a plane with accumulated ice.

In general the objects of this illustrative practice of my invention are accomplished by arriv-y ing at a mathematical expression which reflects the aerodynamic state of the aircraft and which is suitable for functional representation yby .a combination of cooperating instrumentalities that continuously respond to changes in pertinent flight factors. In the preferred practice of the invention I employ an accelerometer in combination with an air speed indicator, or the equivalent of such a combination, to evaluate the selected expression continuouslythereby to indicate the instant aerodynamic state, and I further provide a reference or index to indicate the relation of the instant aerodynamic state to stall conditions, i. e., to indicate the instant margin of safety.

The above and other objects of my invention will be apparent in the following description of my invention taken with the accompanying drawings.

In the drawings, which are to be regarded as merely illustrative,

Fig. i is a diagram representing an aircraft in side elevation and showing relationships involved in the practice of the invention;

Fig. 2 is a graph showing lift and, drag co eiiicientsfor different angles ofY attack;

Fig. 3 is a diagram illustrating the principle of an accelerometer that may be employed in the practice of the invention;

Fig. 4 is a diagram means that may be om? ployed for mechanically combining factors in the practice of thenvention; andY Fig. 5 is a simplified diagrammatic view in An understanding of the invention may be approached advantageously by rst lconsidering Ia mathematical analysis leading to an appropriate basic expression.

In Fig. 1,

a', y coordinates are chosen .as fixed with respect to the aircraft .iz-axis is chosen parallel to axis of propeller shafts y-axis is perpendicular to -.axis and to a vline drawn from tip to tip of wing.

L is the lift component of aerodynamic force on wmg.

D is the drag component of aerodynamic 'force on wing.

.M :the moment of the aerodynamic force on wing about a particular spanwise line through .the airfoil Aat the aerodynamic center.

YLeDtMi; .LfDfMf `are the lift drag and moment components of the :aerodynamic forces acting on the .tail lplane and fuselage respectively.

'T .is the prope'ller thrust.

W is the gross weight of the aircraft.

a lis v.the angle of attack, which is the angle be- -tween :the chord line and the line 'of ight.

:at-ip or the angle between the :c-axis and the line of ilight.

.gb is lthe angle between the chord line and the .11:-

`axis.

L=GLAp iis `a representative area `of the wing, .vp .is :the

mass density of the air, V is thetruefair speed. Them V2 2L=CL cos (a-1,b)Ap

V2 2D=CD sin (a-gl/)Ap fSubstitutingin Newtons law of motion,

2Fy=May the following is obtained:

2 Z c. :cos i-wflp-JVC'D sin (wim/)Y- W Wisin =a 'is 'a dimensionless Acoefficient derived from Vthe component of all aerodynamic forces acting Von the plane, inthe -y-direction. Then:

tra

from which I derive the following expression on which I may base the practice of my invention:

CHLD

The manner in which the value of C'LD, i. e., the Value of the derived basic expression, varies with the angle of attack of a particular airfoil is indicated in Fig. 2. Fig. 2 is derived from the coeflicients for NACA Airfoil No. 2412 given in NACA Technical Report 460. The conditions of l.the test were as follows:

Span-infinite Velocity 68 ft./sec.

Pressure 21 atmospheres i Let `l/:O J/=angle between chord line and :r-

axis) (unprimed coefficients are for airfoil of span.)

The maximum value of CLD (which corresponds to the stall condition) isa function of Reynolds number Rzpm where ,u is the coeiiicient of viscosity of the air. The variation of (CLnlmax with change in R is, however, small and depends on the airfoil used. '(CLmmax varies from 1.2 to 1.4 for many common airfoil sections when R varies from 200,000 to 3,500,000. Some airioils have a larger variation and some much smaller.

The basic expression is admirably suited for my purpose because changes in value of the numerator can be followed by various instrumentalities and changes in values of the denominator-.likewise can be followed by various instrumentalities. Thus the numerator varies as a function of the sum of weight force plus acceleration force, or again as a function of wing strain, Ior again as a function of wing stress resulting from mass considerations, i. e., gross weight of the aircraft vas one mass consideration and acceleration as another mass consideration. The denominator varies with a function of the product of mass density of air and true air velocity, or again as the difference between Pitot tube pressure and static tube pressure, or again as a function of indicated air speed. It follows that various instrumentalities may be used to reflect changing values of both the numerator and the denominator in Various practices of my invention and I am not limited to the particular instrumentalities that are described herein by way of example.

The denominator can be measured by means of the Pitot-static tubes of a conventional airspeed indicator since A is constant for a given aircraft and V2 p-=p. -p a=the dllierence between Pitot and static pressures. (No altitude correction is required.)

I'he numerator,

'can be obtained from an accelerometer as follows. spring supported mass, be mounted in the aircraft in such a way that the mass is free to move in the direction of the y-axis only, and mounted at the center of vmass of the aircraft. However, for practical reasons it probably must be mounted on the instrument panel forward of the center of mass.

In Fig. 3 the y-axis is parallel to the ll-axis of the aircraft in Fig. l. The .r-axis is parallel to the :u-axis in Fig. 1. A is the distance the spring is stretched from its unstressed position.

Applying Newtons law along the IJ-axis, positive upward:

The accelerometer displacement,

is a constant of the instrument which for accuracy must have such a magnitude that the natural frequency of the accelerometer is at least twice as high as the highest frequency of the accelerations to be recorded. The natural frequency of the accelerometer is given by the relation To relate the basic expression,

W sin c) C'LDT-'M-g V2 to physical instrumentalities, namely an eccelerometer and an air speed indicator, the numerator may be changed as follows, W being treated as a constant for the present purpose:

A1 is the deflection of the end of the lever system moved by the accelerometer.

n3 is aconstant-the lever ratio of any multiplication system required=A/A1 In the same manner the denominator may be. changed as follows:

V2 p O=7L1A=7L17L2A1 where and the denominator, my basic expression for CLn becomes Let an accelerometer, consisting of a.

A1 and A1 are independently variable and all other terms on the right hand side are constants with the exception of W. If W is treated as a constant, as in practice it may be treated, at least for short periods of time when W varies only with fuel consumption, it is necessary only that the required stall-warning device indicate changing values of the ratio i. e., the resultant of the effects of A1 and A1.

The preferred form of the indicating mechanism Within the scope of my invention various expedients may be employed to determine and/or to indicate the changes in the instant values of this ratio. In the preferred practice of my invention I use an accelerometer, as above described, in combination with the conventional air speed .indicator of the aircraft thus giving the The principle involved in such a mode of cooperation between an accelerometer and an air speed indicator may be readily understood by reference to Fig. 4.

In Fig. 4 the lever AC of length Q is pivoted at A and carries a slider or similar construction B representing the control point for the lever AC. The horizontal displacement of B from A is governed by the differential pressure on the bellows of the air speed indicator and is equal to A1. The vertical displacement of B relative to A is governed by the accelerometer and is equal to A1. If the vertical displacement of C is given by 1 then for small angular displacements of C relative to A Comparing this equation with the above equation for CLn it is evident that CLD is proportional to I.

It is evident from the above equation that an instrument built along such lines must have a lower limit set on values of A1 because as A1 becomes small l1 becomes very large (if A1 is not zero). If A1 is zero then as A1 approaches zero I' becomes indeterminate and may take any value.

An instrument built along the above lines would have a linear scale of lift coeflicient if the displacements of the lever system involved are linear.

In order to prevent damage to an instrument such as described below, the maximum value of A1 must be fixed so that the maximum A1 when A1 is minimum will not cause 1T to be larger than permissible.

A mechanism for embodying the principle illustrated by Fig. 4 may be constructed in the manner indicated by Fig. 5. Fig. 5 is diagrammatic escasos and for simplification omits various mechanical details such as counterbalancing 'means and hair springs which need xnot :be recited or .explained to those skilled in the art.

The essential 'parts of the mechanism shown in Fig. V'5 -a're van accelerometer generally designated d0., an air speed indicator generally designated H, and a stall-warning indicator generally designated l2. The stall-warning indicator l2 includes a rotary means .in the form of an arm I5 adapted to respond to both the accelerometer and the air speed indicator, the arm l5 corresponding to the arm AC of Fig. 4.

'Ilhe specific .accelerometer li! selected by way of example includes a Weight l carried by an arm i1 extending Vradially from a shaft I'8, `the weight being movable about'the axis vof the lshaft in an arcuate path 'between an upper stop A2li) and a lower stop E! to indicate the magnitude of acceleration. Under conditions of no acceleration, the weight -is maintained =in its `neutral position by virtue of l'a 'pair fof opposed springs iS. The shaft I8 carries a gear segment 22 v-in mesh with a `pinion 23 on a handstaif 25. The handstaf carfriesfa -pointer26 that traverses a suitably gradi uateddial 2l.

For Aproviding a component of motion and `transmitting the component to the arm l5, the shaft I8 is shown with a radial arm '28 from which a link at extends downward `to a spindle 3l, the

spindle carrying a small :roller 32 `in operating contact with the arm l5. -Itis apparent that the small roller 32 corresponds functionally to the slider B of Fig. 4. Thespindle 3l is mounted on a link 33 that is operatively connected to the air speed indicator l in a manner that will be ex- -plained The :airspeed indicator 5H may be fof the '.conventional type including a bellows 3.5 from lwhich a tube 3S extends in the usual manner to .the :pressure Pitct line of :a Pitot tube (not shown). To :permit :proper functioning .of the :bellows 35i, .the entire mechanism is enclosed in .an airtight c, 'ri-ng Si vented V t'lflrough a tube 3B .to the .static .eicf the Pitot static tube.

`.A :suitable .shaft fill is `operatively connected to V'the bellows 3% by means lof a radial arm .si .and la link d2 to a :small bracket `on :the bellows. AFor indicating :air speed, the shaft (il) has -a `radi-alarm 15'5 .connected 'by a link it@ to a radial arm 45 of a shaft il?. The shaft carries a gear segment d8 in mesh with a pinion 56 on a handstaff 5i, the handstai carrying the usual pointer 52 in front of an air speed dial 5S.

In addition .to actuating the pointer 52, the shaft 150 .actuates the link S3 .carrying the roller 3l. To this end the shaft it is adapted to operate a shaft 55 coaxial therewith by Ameans of an angular arm .'55, the arm being arranged .to cause clockwise rotation of the shaft 55 :but not counterclockwise. A spring 5i acting-on-anarm .53 causes the shaft 55 to remain -i-n synchronism with the shaft iii within a range limited by a Vstop screw d carried by a fixed means ci. The stop screw 6a) is in the path vof ,an arm that `.extends radially ,from the shaft 55 :and is pivotally connected to the previously mentioned link 33.

t Ais apparent that the roller 32 serves as a control point .for determining the angular position of the arm I5, and that the vertical distance of this control point from the axis of rota- .tion of thefarm :l5 is ygoverned Vby the accelerom- `eter la@ :and the horizontal ldistance 'is governed :by thefairfspeedgindicator Irl. The angular posi- 8L tion :of the .arm will .therefore vary with the instant value-of the ratio 'The arm 2|5 may itself be employed as the yindicator for proximity to stall conditions but I prefer .the .arrangement shown in which the shaft 59 carrying the arm I5 also carries a gear segment 63 inimesh'with a pinion 65 on a handstarf .56, 'the handstaif carrying .a suitable pointer 61. The .pointer indicates values on a fixed dial face 68.

The relative proximity of the aerodynamic state of the aircraft to stalling condition may be indicated by the position or angle of the pointer 67 relative to a lsuitable reference or stalling index. In my preferred arrangement I make such an index `or reference adjustable relative to the dial to compensate for variations in the gross weight of the aircraft. Thus, in Fig. 5 I employ a reference or vindex member 'I0 in the form of a bent pointer mounted on a gear Il mounted concentrically behind the fixed dial face 68. The gear 'H is in mesh with a pinion 12 on a shaft 'i3 that may be manually controlled by a suitable knob' 1:5 onthe instrument panel. For guidance in vsuch compensating adjustment for .changes in :thegross weight, the face of the gear Irl may be vgraduated in terms of gross weight, ythe numerals of which may be registered with and viewed through va small window 1B .in :the dial face 68.

M ode of :operation The manner in which the preferred form of the invention operates will be readily understood from the foregoing description. It is merely necessary for fthe-plotito `observe from time to time the position of the pointer el relative to the reference member Til to be informed of the margin of safety relative to stall conditions. Since the. accelerometer and the air speed indicator operate with .substantially Vno lag in response .to changes in the magnitude .of acceleration and air speed, .the position `of `.the pointer 61 represents substantially the instant value of the lift coefficient CLD.

At the beginning of a fiight the knob 'i5 is manipulated to position the reference member 'f in accordwith the gross weight of the aircraft at take-off. During flight the jpilot will manipulate the knob it from time to vtime to compensate 'for consumption of fuel and oil by the 'aircraft engines. Such compensation may be made .continuously vby suitable automatic means. If the net load drops suddenly in the course of night, as when a load of bombs .is released, the pilot will shif-t l.thefreference member 70 accordingly.

In this preferred form of the invention the stall indication pointer El Vis .associated with a dial t8 having linear graduations. The .scale of graduations ,may be purely arbitrary or, if desired, the .scale may .be so chosen as `to indicate actual Values of lift coefficient, Cmn for a given magnitude .-.of Ygross weight.

While the described arrangement provides for a simple ,visual .indicatonfor guidance of the pilot, .,it..`.`will be readily .understood by those skilled in the art' that Various signal expedients -may-be`employed." v

An important feature of the invention is that it offers the pilot means to ascertain the exact aerodynamic effectof icingand thereby to ascer tain the margin of safety available in maneuvering the aircraft to a landing. When the wings become iced, the pilot may stall his plane ata safe altitude in such manner as to ascertain the stall position of the pointer 61. Having ascertained the stall point under ice conditions, the pilot may either keep the stall point in mindor may manipulate the knob 15 to the new stall point for `guidance in landing the airplane, making suitable allowance for continued ice formation. If a maximum-indicating pointer ll with a reset knob 18 is added, as shown in Fig. 5, the added pointer will be automatically moved to the danger point by the trial stall of the iced aircraft thus simplifying the pilots task of ascertaining the narrowed margin of safety.

While the described form of the invention is in effect a triple instrument with three dials for indicating acceleration, air' speed, and lift coefhcient, respectively, either or both of the dials for acceleration or air speed may be omitted leaving a single dial for lift coefficient..

Since the pointer 6T indicates variations in the value of the life coefficient CLD, the pointer may be employed to indicate the instant value of any factor or effect that varies withthe value of C'Ln. For example, the dial 62 may be provided with a scale to indicate angles of attack. Obviously the mechanism may also be modified to indicate the instant value of factors or effects that vary inversely as the lift co-efcient CLD. l

While the particular practice of the invention set forth in detail is directed primarily to ascertain the aerodynamic states accompanying variation in pitch or the angular position of the aircraft about a transverse axis, it will be readily understood that the same principles may be based on or related to the attitude of the aircraft with respect to other axes, such as the c: and t/-axes mentioned above.

, The preferred form offmy invention described in specific detail herein will suggest to those skilled in theart various changes and substitutions under my basic concept and I reserve the right to all such departures from the described form of the invention that properly lie within the scope of my appended claims.

I claim:

l. A device of the character described to indicate the instant effect of aerodynamic forces on an aircraft relative to the effect of the aerodynamic forces on the aircraft under given conditions comprising a first means responsive to acceleration forces affecting the stressing of the wings of the aircraft, a second means responsive to changes in dynamic pressure on the aircraft, indicating apparatus including an indicator operatively connected to said rst means and said second means, said apparatus being responsive solely to changes in the ratio between the response of said first means and the response ofY determine the instant aerodynamic state of an aircraft, the combination of means rotatable about a fixed axis through an angular range of positions representing a progressive series of aerodynamic states, a control means operatively connected with said rotary means to determine the angular position thereof, said control means being movable in two dimensions for regulation of the rotary means, means to move said control means with respect to one of said dimensions in response to changes in acceleration force affectingr the stressing of the aircraft wings, and means to move said control means with respect to the other said dimensions in response to changes in the dynamic pressure on the aircraft.

3. In an aircraft instrument having an air speed indicator and an accelerometer indicator, the combination therewith of a stall warning apparatus operatively connected to said two indicators, said connection comprising a pointer shaft, means for rotating said shaft, an instrumentality for operating said means, a first transmission means for feeding into said instrumentality responses from said air speed indicator, a second transmission means for feeding into said instrumentality responses from said accelerometer indicator, said instrumentality including means responsive to changes in the ratio between responses from said two transmission means for actuating said shaft rotating means both vectorally and quantitatively in relation to changes in such ratios. n

4. In an aircraft vinstrument having an air speed indicator and an accelerometer indicator,

the combination therewith of a stall warning apparatus operatively connected to said two indicators, said connection comprising a pointer shaft, means for rotating said shaft, an instrumentality for operating said means, a rst rtransmission means for feeding into said instrumentality responses from said air speed indicator, a second transmission means for feeding into said instrumentality responses from said accelerometer indicator, said instrumentality including means responsive to changes in the ratio Y between responses from said two transmission means for actuating said shaft rotating means both vectorally and quantitatively in relation to changes in such ratios, and reference means adjustably positionable relative to said pointer shaft for indicating stall conditions in relation to changes in the gross load of the aircraft.

WlLLIAM NICHOLS FINDLEY.

REFERENCES CTED The following references are of record in the file of this patent:

UNITED STATES PATENTS 

